Ultrafast piezocapacitive soft pressure sensors with over 10 kHz bandwidth via bonded microstructured interfaces

Flexible pressure sensors can convert mechanical stimuli to electrical signals to interact with the surroundings, mimicking the functionality of the human skins. Piezocapacitive pressure sensors, a class of most widely used devices for artificial skins, however, often suffer from slow response-relaxation speed (tens of milliseconds) and thus fail to detect dynamic stimuli or high-frequency vibrations. Here, we show that the contact-separation behavior of the electrode-dielectric interface is an energy dissipation process that substantially determines the response-relaxation time of the sensors. We thus reduce the response and relaxation time to ~0.04 ms using a bonded microstructured interface that effectively diminishes interfacial friction and energy dissipation. The high response-relaxation speed allows the sensor to detect vibrations over 10 kHz, which enables not only dynamic force detection, but also acoustic applications. This sensor also shows negligible hysteresis to precisely track dynamic stimuli. Our work opens a path that can substantially promote the response-relaxation speed of piezocapacitive pressure sensors into submillisecond range and extend their applications in acoustic range.

Supplementary Text 1.The design of digital circuit board.The capacitance measurement circuit is mainly composed of five modules: power supply, range switching, capacitance measurement, microcontroller, and high-speed communication (Supplementary Fig. 4b).The power module is used to provide a stable +3V DC power supply to other modules and consists mainly of a power switch and a low noise TPS79330 linear regulator.The capacitance measurement module is the heart of the circuit.As shown in Supplementary Fig. 4a,  The capacitance measurement module uses a precision timer (SE555) to generate a pulse (Supplementary Fig. 4c).The duration of the high-level pulse generated by the module varies according to the capacitance being measured.When the SE555 receives a low-level control signal at the trigger input, it initiates the production of the high-level pulse.The duration of this high-level pulse, denoted as th, depends on the time constant of the RC network.
The charging and discharging resistance of the RC network, denoted RA, is finely tuned by the range switching module.This module provides four selectable levels of high Utilizing finite element simulations with varied contact length ratios, we derive the changes in contact length (a0), height (h), and bottom pressure (P) of the bonded structure during loading up to 400 kPa.By integrating the aforementioned equations (3) -(7) and performing differential summation, we calculate the capacitance of the microstructure both before loading (C0) and during loading (C).Subsequent data analysis enables the determination of the sensitivity (∆C/C0) of the bonded microstructure concerning variations in loading pressure under different length ratios.

Supplementary Figure 4 .
Schematic design diagram of the digital circuit board.a, Schematic diagram of capacitor charging and discharging circuit and the correspondence between capacitance value and charging time.b, The capacitance measurement circuit that is mainly composed of five modules: power supply, range switching, capacitance measurement, microcontroller, and high-speed communication.c, Schematic diagram of capacitor charging and discharging circuit and the correspondence between capacitance value and charging time.Supplementary Figure 5. Diagram of power supply module and microcontroller module of the digital circuit board.a, Schematic design diagram of power supply of the digital circuit board.b, Schematic design diagram of the microcontroller module of the digital circuit board.
the capacitance value is measured via the charging time of the sensor under a specific DC voltage and resistance condition.A complete measurement cycle consists of capacitor charging and discharging.During the charging phase, switch S2 is open, and S1 is closed, controlled by a precision timer (SE555).The DC power supply UE charges the measured capacitor C through the resistor R. The capacitance value is calculated by measuring the time that the capacitor takes to charge to a certain voltage U0.During charging, the voltage across the measured capacitor rises exponentially with time.At a constant power supply voltage UE and charging resistance R, the charging time depends solely on the measured capacitor.The larger the capacitor, the longer the charging time.Therefore, based on the measured charging time, the capacitance value can be calculated.
precision resistors: 330, 100, 33, and 10 kΩ.In the RC network, C is the total capacitance, consisting of the intrinsic capacitance C0 of the circuit and the external capacitance Ce to be measured.Consequently, with fixed and known values of RA and C0, the measured capacitance Ce can be calculated by measuring the duration of the high-level pulse using equation(1).The microcontroller module controls the operation of the entire circuit and sends the measurement results via the communication module (Supplementary Fig.5b).It consists of an STM32F405RGT6 microcontroller and peripheral circuits such as a quartz oscillator, reset, SWD download and LED display.When it is necessary to measure the capacitance, the MCU first receives the command from the external host computer to control the on-off of the range switching module relay to select the appropriate measurement range, then sends a low-level control signal to the capacitance measurement module, and at the same time starts the counter inside the MCU to start time the high-level pulse output by SE555, wait for the end of the high-level pulse to get its duration th, and calculate the measured capacitance value by formula (1) to complete a measurement.The charging time for the capacitor to charge to a certain voltage U0 is determined by UE, R and C. According to the actual test results, the charging time exceeding 20 μs can avoid additional errors caused by too fast charging rates.For the charging time measurement accuracy, Csensor + Cwires + Ccircuit ≈ 200 pF, and the minimum capacitance change that needs to be resolved is 0.05 pF.Therefore, the required resolution is at least 0.05/200×100% = 0.025%.The frequency of the precision timer is 1/168 μs.When the charging time is 25 μs, the count is 4200 times (25×168).The resolution is 1/4200×100% = 0.02%.In terms of capacitor discharge time, in order to avoid interference with the next capacitor measurement and cause cumulative errors, it is necessary to ensure that the voltage across the capacitor is discharged to zero as possible.Therefore, the discharging time is controlled above 10 μs.Therefore, considering all the above factors, the capacitance measurement period cannot be less than 25 + 10 = 35 μs, otherwise it will bring significant errors to the measurement.Taking into account the margin for other limiting factors such as data processing and switching time (5 μs), the measurement time is about 40 μs, resulting in a measurement frequency of 25 kHz.subsequent calculation of the overall microstructure capacitance and sensitivity, we neglect the air capacitance and approximately equate the dielectric layer capacitance (Cd) to the overall structure capacitance (C).During the loading process of the overall structure, the compressed height of the dielectric layer's top contracts, the bonded contact length gradually increases, and the overall capacitance progressively rises.Simultaneously, the overall pressure of the structure gradually increases, as shown in Supplementary Fig. 17.For cylindrical dielectric layers at different positions, pressures and relative permittivities are calculated using the form of equal forces on each cross-section: {   =  2 4 2  = 98.11 0.0003532  − 76.89 −0.02481  (7) Combining equation (3), we obtain expressions for the relative permittivity of cylindrical dielectric layers at different positions along the height direction.Supplementary Figure 17.Geometric dimensions and capacitance calculation before and after the compressed loading process of the bonded micro-cone structure.a, Bonded structure unloaded.b, Bonded loading process with pressure applied at the bottom as P.